Pre-assessment of linear equations knowledge from graphical data

Five students in SC 130 Physical Science were given a pre-assessment of their understanding of linear equations which focused on the interpretation of graphical and tabular presentations.

Four of the five students had completed MS 100 College Algebra, the remaining student had completed MS 099 Intermediate Algebra. 

Three students either left questions blank or provided wrong answers to every problem. Two students successfully answered six and eight of nine questions respectively. These are bright young students who have had at least twelve years of mathematics including high school algebra and collegiate math courses. The one student in MS 099 Intermediate Algebra was the student who answered six of nine correctly. In some sense, that the level of mathematics did not predict success is an indictment of the failure of the mathematics curriculum to teach mathematics. And when asked if they like math class, only two students responded that they did. Most students are only all too happy to have math classes in the rear view mirror of their lives.

My grandson just graduated early childhood education (kindergarten). Prior to graduation he was telling me about mathematics. He explained 2+2 is 4, 4+4 is 8, 8+8 is 16. I was suitably impressed - he is only five after all. Then he noted that 64 plus 64 is 128. I thought I misheard him, so I asked him to say that again. Which he dutifully did.

So I thought I would show him that some of those numbers can make squares. I used little coconuts to make a 2 × 2 square. Then expanded to a 3 by 3 square with nine coconuts on the ground.

I was going to add seven more coconuts when he said. "And four fours is sixteen." I was just starting to say, "Well done!" When he commented, "100 is also a square. Ten tens" I was stunned. Then he noted that 36 is both a square and a step squad number. He had to explain the step squad numbers to me, and did so quite patiently. He explained that 21 is a step squad number, as is 28 and 36. Then he noted that 36 is the only step squad number that is a square. I was still scrambling to figure out the pattern when he noted that 45 is also a step squad number, as is 55. Which, he said with an air of conclusion, is five elevens. While I was still trying to comprehend what the step squad numbers were he began talking about even top and odd top numbers, and super rectangle numbers like 12, wrapping up with the multiples of ten through to one hundred.

I began to realize that this must be coming from somewhere because he was intoning the multiples of ten in a sing song manner. Over the next few days I came to realize that he was picking this up from YouTube math videos for children.

Watching my grandson operate in math that one would expect to be beyond his level at five years old suggests that creative, alternative, and engaging ways to deliver curriculum can carry a student farther in quantitative reasoning that one might expect for their age and maturity. He loves mathematics and math facts, often wandering around the yard spouting off one or another multiplication table. 

I would guess that the next 12 years of drill and kill textbook mathematics will absolutely destroy his interest in mathematics. Math teachers eat their own children. Mathematician Edward Frenkel has noted the destruction of any love for mathematics by the current curriculum in his book Love and Math: The Heart of Hidden Reality. In fifteen years my grandson will probably be equally unable to answer simple questions about linear equations. 

Of course math education is always undergoing a new revolution. Forever. New math in the 1960s was not the first call to re-envision the math curriculum. Later would come the NCTM standards documents and more recently common core mathematics. And yet math texts and math teaching plug along in the same manner as they have for perhaps 400 years, maybe more. Math curriculums keep doing the same thing decade after decade and wonder why the results do not differ. 

I do not pretend to have the answers, but I can see a world of possibilities in my grandson and the curriculum he is on. I hadn't opened Desmos in a while, I see that the desktop version has a raft of new function capabilities, including lists. In the spirit of showing that 36 is a step squad number and a perfect square, I generated:

https://www.desmos.com/calculator/ofzcxlim7s

Those step squad numbers are just the triangular numbers which are also the sum of the first n numbers. And lest one think so, my grandson is not gifted - he is simply. learning from engaging videos that he watches. By any math curriculum specialist's estimation he grade levels above kindergarten, but again, that is just another indictment of the way math is taught. First grade addition, multiplication tables by third grade. Drill and kill. No heroes, all zeroes (the multiples of ten are all heroes with zeroes for those who are in the know).